Regularização e conjuntos minimais para sistemas dinâmicos não suaves

Author(s)

Douglas Duarte Novaes

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2015-06-07

Examining board members

Marco Antonio Teixeira; Jaume Llibre Salo; Daniel Smania Brandão; Paulo Ricardo da Silva; Claudio Aguinaldo Buzzi; Ricardo Miranda Martins

• Advisor: Marco Antonio Teixeira; Jaume Llibre

Abstract

The problems discussed in this thesis focuses mainly in the theory of nonsmooth differential system. Several topics of this subject are treated. The main results may be resumed as following. First, the hypotheses of the classical averaging theorems are relaxed to compute periodic solutions of nonsmooth differential systems. Second, regarding planar piecewise linear differential system with two zones it is shown that oscillating the line of discontinuity several configurations of limit cycles can be obtained. In addition it is proved that for a given natural number n there exists a planar piecewise linear differential system with two zones having exactly n limit cycles. Moreover, using the Chebyshev theory, it is established sharp upper bounds for the maximum number of limit cycles that some classes of planar piecewise linear differential systems with two zones can have when the set of discontinuity is a straight line. Third, the concept of sliding Shilnikov orbit is introduced in the context of Filippov systems, then the Shilnikov problem is considered for this case. Finally, the recent extensions of the Filippov's conventions for solutions of discontinuous differential systems is studied and some results concerning its regularization are established. Moreover the pinching of continuous systems is studied in the context of these new conventions (AU)

• FAPESP's process: 12/10231-7 - Regularization and minimal sets for non-smooth dynamical systems
• Grantee: Douglas Duarte Novaes
• Support Opportunities: Scholarships in Brazil - Doctorate